Simplify the following expression: $ q = \dfrac{r + 6}{-2r - 3} + \dfrac{-7}{4} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{r + 6}{-2r - 3} \times \dfrac{4}{4} = \dfrac{4r + 24}{-8r - 12} $ Multiply the second expression by $\dfrac{-2r - 3}{-2r - 3}$ $ \dfrac{-7}{4} \times \dfrac{-2r - 3}{-2r - 3} = \dfrac{14r + 21}{-8r - 12} $ Therefore $ q = \dfrac{4r + 24}{-8r - 12} + \dfrac{14r + 21}{-8r - 12} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{4r + 24 + 14r + 21}{-8r - 12} $ $q = \dfrac{18r + 45}{-8r - 12}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{-18r - 45}{8r + 12}$